1. Field of the Invention
The present invention relates to petroleum exploration and more particularly, to the study of fluid flows within an underground formation.
2. Description of the Prior Art
Basin modelling reconstructs the geological history of a sedimentary basin and its petroleum systems in order to help locate hydrocarbon traps, that is the reservoirs, to assess the amount and quality of the trapped hydrocarbons, and finally to assess the risks of encountering excess pressures while drilling. Reservoir simulation studies the evolution over time of the proportions of water, gas and petroleum in the reservoir so as to appreciate the cost-effectiveness, to validate or to optimize the position of the wells providing smooth operation of the reservoir development.
In times where sustainable growth and environmental protection have become essential, a third important study linked with petroleum exploration is to carry out simulations for injecting CO2 into porous media.
Basin modelling, reservoir simulation and CO2 simulation are techniques based on flow simulation in a porous medium. These simulations are performed by a partial-differential equation system by finite-volume methods on a mesh describing the geometry of the underground medium. Today, exploration is interested in complex geometry zones with many faults of random position. Automatic generation of a 3D mesh that can represent this geometrical complexity is the first essential stage towards elaboration of the simulation software, which is the flow simulator, for such a medium, from the horizons that delimit the various geological layers and the faults that intersect the horizons. The horizons and the faults are provided as surfaces, triangulated from a pattern of points. These points generally result from seismic surveys. Considering the flow simulators used in the industry, the mesh has to comprise as many hexahedral elements as possible to allow a better simulation result to be obtained, and meshing has to be done between the horizons in order to respect the infrastructure of the medium.
In the field of petroleum exploration, most current porous medium flow simulators work with regular or “Scottish Cartesian” grids. In order to try and adjust the meshes to the faults and to any heterogeneity form, as a simulation calculation support, there are known techniques such as local grid refinement, CPG grids (described in French Patent 2,747,490 for example) or grids with vertical split nodes.
The meshes described above are based on grids. They are quasi structured, that is their topology is fixed. Each internal vertex is incident to a fixed number of mesh cells and each cell is delimited by a fixed number of faces and edges. They are therefore only suited to a relatively simple geometry. For a basin simulator, for each given age, a mesh is generated by stacking layers, on a single 2D grid (map), connected by verticals. Mesh generation is advantageously very simple. However, it is impossible often to represent oblique faults.
In order to enable fault management, there are methods that first perform manual decomposition by blocks along the faults and then generate a simple mesh for each block. This approach is however not totally suited for flow simulation in a complex geometry medium for two reasons. First, the quality of the elements is not satisfactory for irregular geometries, and second, with the random presence of many faults, it is nearly impossible to perform manual decomposition of the medium processed.
In order to capture the entire complexity of the medium geometry, it is also possible to generate an entirely unstructured mesh, with a completely arbitrary topology. A vertex of the mesh can belong to any number of cells and each cell can have any number of edges or faces. Meshes of PErpendicular Blssector (PEBI) or Voronoi type, are proposed in the following document.                Z. E. Heinemann, G. F. Heinemann and B. M. Tranta, “Modelling Heavily Faulted Reservoirs”, Proceedings of SPE Annual Technical Conferences, pages 9-19, New Orleans, La., September 1998, SPE.        
Although unstructured meshes describe complex geometries well, they, unlike structured meshes, are very difficult to construct, to handle and to store, unlike structured meshes. In order to reconcile the advantages and the drawbacks thereof, approaches referred to as “hybrid” have been proposed, which use unstructured meshes only in complex geometry zones. However, joining together unstructured and structured meshes remains a difficult task.
Finally, there are four main categories of methods for automatic generation of hex-dominant meshes:                octree/grid methods,        plastering methods,        block methods,        sweep methods.        
The principle of octree/grid methods wraps the domain to be meshed in a grid and subdivides a cube recursively until the geometry of the domain is well captured. That is, until the cell size criterion, which essentially depends on the minimum distance of the points from the contour and on the available resources, is met. Tetrahedral or hexahedral elements are then created at the intersection of the surfaces of the domain by following some intersection patterns.
Octree/grid methods are advantageously computer automated and applicable whatever the geometry. However, the mesh that is generated is not in accordance with the shape of the domain. Furthermore, when the contour is irregular, a time consuming intersection calculation is inevitable and a substantial expansion of the number of cells may occur to reach a good boundary approximation precision.
Plastering methods fill the volume of the domain with 3D elements from the initial surface front of the model by advancing towards a center by starting from the new front that has been constructed. The procedure is complete once the front becomes empty.
In plastering algorithms, it is difficult to determine the order of front advance, and to detect and to process the collision and divergence zones. These methods are thus considered to not be robust especially when complex geometries are concerned. As a result, obtaining a mesh of good quality is not guaranteed.
Block approaches decompose the concerned domain into coarse blocks having an elementary topology (triangle, quadrangle, tetrahedron, pentahedron and hexahedron and then meshing each block independently using algebraic methods or by solving PDEs (partial-differential equations), and in eventually joining the blocks together to form the global mesh of the entire domain.
The major advantage of block methods is that it is trivial to mesh once the partition is achieved. Furthermore, it is possible to solve in parallel the problem on each block. However, the partition itself remains very time consuming and difficult to be automated, and inter-block interfacing has to be carefully managed to ensure conformity of the final joining.
Sometimes considered to be “2.5D meshes”, sweep methods “sweep” a quadrilateral mesh by following a curve. Regular hexahedra layers are formed at specified intervals using the same topology as the quadrilateral mesh. This technique can be generalized in order to mesh volumes of some classes by definition of the source and target surfaces.
The meshes generated by sweep methods are automatically aligned with the interfaces, which is of course a great advantage. However, these methods are not well suited to the simulation of the porous medium, where the topology change can go from one horizon surface to the next due to the interference of the faults.